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C22×C3×C4×C7×C29 #72188457

order9744
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 64512
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C4×C7×C29
multiplicative(ℤ/11977)ˣ, (ℤ/12685)ˣ, (ℤ/14455)ˣ, (ℤ/15399)ˣ, (ℤ/17661)ˣ, (ℤ/19496)ˣ, (ℤ/23548)ˣ, (ℤ/23954)ˣ, (ℤ/25370)ˣ, (ℤ/28910)ˣ, (ℤ/29244)ˣ, (ℤ/30276)ˣ, (ℤ/30798)ˣ, (ℤ/35322)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C3×C7×C29
socle, prime radicalC23×C3×C7×C29C2
LCSG ▷ C1
UCSC1 ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9744 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C7×C8×C29, C2×C3×C42×C7×C29, C23×C3×C4×C7×C29, …
maximal normal subgroup ofC22×C3×C7×C8×C29, C2×C3×C42×C7×C29, C23×C3×C4×C7×C29, …
maximal quotient ofC22×C3×C7×C8×C29, C2×C3×C42×C7×C29, C23×C3×C4×C7×C29, …
automorphism group ofC5×C43×C59
outer automorphism group ofC5×C43×C59

GAP

Past the SmallGroups library coverage — no SmallGroups id.